From 20340b940cc19fb406f9978b40d2ea1eed8c6349 Mon Sep 17 00:00:00 2001
From: aburt2 <32888184+aburt2@users.noreply.github.com>
Date: Fri, 27 Oct 2023 14:45:20 -0400
Subject: [PATCH] fixed up math rendering

---
 docs/Availability Modelling.md  |  67 ++++++++++++++++----------------
 docs/Images/IDMIL-logo-icon.png | Bin 0 -> 11283 bytes
 docs/Images/favicon.ico         | Bin 0 -> 15406 bytes
 docs/index.html                 |   7 ++--
 4 files changed, 37 insertions(+), 37 deletions(-)
 create mode 100644 docs/Images/IDMIL-logo-icon.png
 create mode 100644 docs/Images/favicon.ico

diff --git a/docs/Availability Modelling.md b/docs/Availability Modelling.md
index 0fa9dd2..7dee010 100644
--- a/docs/Availability Modelling.md	
+++ b/docs/Availability Modelling.md	
@@ -12,8 +12,7 @@ TBD
 | Performance Intensity   | $j_p$      | The intensity of the performance, rough indicator of the impact of a performance on the reliability of certain components                                                                                     |
 | Performance Frequency   | $p_f$      | The average amount of performances per month. It can be used along side **maintenance time between performance**, and **technician availability** to compute the interruption percentage. **SIMULATION ONLY** |
 | Technician Availability | $A_{tech}$ | The average amount of hours a technician/luthier is available to fix any issues an artist can’t fix with their instrument per month. **SIMULATION ONLY**                                                      |
-| Technician Turnaround   | $t_{tech}$ | The average amount of business days it takes for the technician/luthier to return the instrument to the artist/musician. **SIMULATION ONLY**                        
-                                          |
+| Technician Turnaround   | $t_{tech}$ | The average amount of business days it takes for the technician/luthier to return the instrument to the artist/musician. **SIMULATION ONLY** |
 ## Model Inputs
 
 | **Inputs**                               | **Symbol** | **Description**                                                                                               |
@@ -28,15 +27,15 @@ TBD
 
 ### 1. Computing MTBF and failure rate of T-Stick
 
-To compute the Practice interruption rate we must first compute the failure rate of the T-Stick ($$ \lambda_{tstick}$$). We do this by adding the failure rate of each component.
+To compute the Practice interruption rate we must first compute the failure rate of the T-Stick ($ \lambda_{tstick}$). We do this by adding the failure rate of each component.
 
-$$$
+$$
 \begin{equation}
 \lambda_{tstick} = \lambda_{esp32} + \lambda_{fsr}+\lambda_{imu}+\lambda_{button}+\lambda_{capsense}+\lambda_{resistor}+\lambda_{touchsensor}+\lambda_{battery}+\lambda_{connectors}
 \end{equation}
-$$$
+$$
 
-where $$\lambda_i$$ is the failure rate of component *i*.
+where $\lambda_i$ is the failure rate of component $i$.
 
 The failure rates for several components such as:
 
@@ -51,78 +50,78 @@ can be estimated using a combination of the [FIDES reliability prediction too](h
 
 We compute the MTBF of the t stick by taking the reciprocal of the failure rate.
 
-$$$
+$$
 \begin{equation}
 MTBF_{tstick} = \frac{1}{\lambda_{tstick}}
 \end{equation}
-$$$
+$$
 
 ### 3. Compute Mean Performances between failure (MPBF)
 
-We can then compute the mean performances between failure ($$MTBF_{tstick}$$) by dividing the $$MTBF_{tstick}$$ by the **performance time (**$$t_P$$)
+We can then compute the mean performances between failure ($MTBF_{tstick}$) by dividing the $MTBF_{tstick}$ by the performance time ($t_P$)
 
-$$$
+$$
 \begin{equation}
 MPBF = \frac{MTBF_{tstick}}{t_p}
 \end{equation}
-$$$
+$$
 
 ### 4. Compute PIR
 
-We calculate the practice interruption rate by taking the reciprocal of $$MPBF$$.
+We calculate the practice interruption rate by taking the reciprocal of $MPBF$.
 
-$$$
+$$
 \begin{equation}
 PIR = \frac{1}{MPBF}
 \end{equation}
-$$$
+$$
 
-Using Eq.5, Eq.6 and Eq.7 we can simplify the PIR expression.
+Using Eq.3 and Eq.6 we can simplify the PIR expression.
 
-$$$
+$$
 \begin{align*}
 PIR &= t_p(\frac{1}{MTBF_{tstick}}) \tag{Using Eq.3}\\
  &= t_p(\lambda_{tstick}) \tag{Using Eq.6} \\
 \end{align*}
-$$$
+$$
 
 Hence an alternative expression for the Practice Interruption rate is:
 
-$$$
+$$
 \begin{equation}
 PIR = t_p(\lambda_{tstick})
 \end{equation}
-$$$
+$$
 
 In simple words the **Practice Interruption Rate** is the:
 
-$$$
+$$
 \text{average performance time} \times \text{failure rate of the t-stick}
-$$$
+$$
 
 ## Compute Performance/Maintenance Ratio (PMR)
 
-Computing the Performance/Maintenance Ratio (PMR) is a matter of taking the $$MTBF_{tstick}$$ computed in the PIR model and dividing that by the average maintenance time.
+Computing the Performance/Maintenance Ratio (PMR) is a matter of taking the $MTBF_{tstick}$ computed in the PIR model and dividing that by the average maintenance time.
 
 ### Computing Average Maintenance time ($$T_m$$)
 
-To compute average maintenance time we consider the mean time to repair ($$MTTR_c$$) of each component and the failure rate of each component ($$\lambda_c$$). We can then take a weighted average of all the repair by taking into account each components contribution to the total failure rate.
+To compute average maintenance time we consider the mean time to repair ($MTTR_c$) of each component and the failure rate of each component ($\lambda_c$). We can then take a weighted average of all the repair by taking into account each components contribution to the total failure rate.
 
-$$$
+$$
 \begin{equation}
 T_m =  \sum_{c=0}^n \frac{\lambda_c}{\lambda_{tstick}}(MTTR_c)
 \end{equation}
-$$$
+$$
 
 ### Compute PMR
 
-To compute PMR we divide the $$MTBF_{tstick}$$ by the average maintenance time ($$T_m$$).
+To compute PMR we divide the $MTBF_{tstick}$ by the average maintenance time ($T_m$).
 
-$$$
+$$
 \begin{equation}
 PMR = \frac{MTBF_{tstick}}{T_m}
 \end{equation}
-$$$
+$$
 
 ## Compute Direct Maintenance Costs (DMC)
 
@@ -130,22 +129,22 @@ We can also look at the direct maintenance cost of the T-Stick which we define a
 
 ### Compute Mean Repair Cost of the T Stick
 
-The mean repair cost of the T-Stick ($$MRC_{tstick}$$) is computed the same way the average maintenance time, by using a weighted average of the mean repair cost of each component.
+The mean repair cost of the T-Stick ($MRC_{tstick}$) is computed the same way the average maintenance time, by using a weighted average of the mean repair cost of each component.
 
-$$$
+$$
 \begin{equation}
 MRC_{tstick} = \sum_{c=0}^n \frac{\lambda_c}{\lambda_{tstick}}(MRC_c)
 \end{equation}
-$$$
+$$
 
 ### Compute DMC
 
-To compute DMC we divide the mean repair cost by the mean time between failure of the T-Stick ($$MTBF_{tstick}$$)
+To compute DMC we divide the mean repair cost by the mean time between failure of the T-Stick ($MTBF_{tstick}$)
 
-$$$
+$$
 \begin{equation}
 DMC = \frac{MRC_{tstick}}{MTBF_{tstick}}
 \end{equation}
-$$$
+$$
 
 
diff --git a/docs/Images/IDMIL-logo-icon.png b/docs/Images/IDMIL-logo-icon.png
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diff --git a/docs/index.html b/docs/index.html
index 7da59f5..df1ec38 100644
--- a/docs/index.html
+++ b/docs/index.html
@@ -7,8 +7,9 @@
     content="width=device-width, initial-scale=1, minimum-scale=1.0, shrink-to-fit=no, viewport-fit=cover">
 
   <!-- Replace with your own title and description. -->
-  <title>Awesome Docsify Site</title>
-  <meta name="description" content="An awesome docsify site for publishing some content on the web.">
+  <title>T-Stick Documentation</title>
+  <link rel="icon" href="Images/favicon.ico" />
+  <meta name="description" content="Website containing documentation related to the T-Stick">
 
   <!-- Default Theme (see https://docsify.js.org/#/themes) -->
   <link rel="stylesheet" href="//cdn.jsdelivr.net/npm/docsify@4/lib/themes/vue.css">
@@ -24,7 +25,7 @@
       name: 'T-Stick Documentation',
 
       // Logo configuration
-      logo: '/Images/IDMIL-logo-new-vector-trBG.svg',
+      logo: '/Images/IDMIL-logo-icon.png',
 
       // Sidebar Configuration
       auto2top: true,